Question

The side of a square land was measured as 150 m and is in error by 0.05 m. What is the corresponding error in the computed area of the land?
1. 5 m²
2. 10 m²
3. 15 m²
4. 20 m²

Answer 1

Correct Answer - Option 3 : 15 m²

Method 1:

Area = (side) ² or A = x²

\(\frac{{dA}}{{dx}} = 2 \times x\)

\(dA = 2 \times x \times dx\) {dx is error in length and dA is error in area}

\(dA = 2 \times 150\; \times \left( { \pm \;0.05} \right)\) = ± 15 m²

∴ Error in area = ± 15 m²   

Method 2:

Initial area = 150 × 150 = 22500 m²

True Length, L = given length ± error

So we get L₁ = 150+ 0.05 = 150.05 m or L₂ = 150-0.05 = 149.95 m

True area, A₁ = (150.05)² = 22515.0025 m² or  A₂ = (149.05)² = 22485.0025 m²

Error = A₁-A or A₂ – A

Error = 22515.0025 – 22500 or 22485.0025-22500

Error = + 15.0025 m² ≈ 15 m² or – 14.9975 m² ≈ -15 m²

We will get same answer.